Abstract
The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.
Highlights
During the past few decades, neural networks (NNs) have received great attention because of their wide applications in various fields such as image processing, signal processing, pattern recognition, associative memory, parallel computation, optimization, and error diagnosis [1, 2]
It is well known that a time delay is inherent in various systems, including NNs, owing to the finite speed of signal transmission and conversion rate of the processors
It is essential to investigate the stability of the neural networks with time delay [5,6,7,8,9,10]
Summary
During the past few decades, neural networks (NNs) have received great attention because of their wide applications in various fields such as image processing, signal processing, pattern recognition, associative memory, parallel computation, optimization, and error diagnosis [1, 2]. One of the most important questions in theoretical analysis of NNs is dynamical behaviors of the NNs, such as their stability, periodic oscillatory, and chaos. It is well known that a time delay is inherent in various systems, including NNs, owing to the finite speed of signal transmission and conversion rate of the processors. It is essential to investigate the stability of the neural networks with time delay [5,6,7,8,9,10]
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